Can You Solve This CLEVER Problem from Narayana Hyderabad Test ? ?
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- Опубліковано 23 лют 2024
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Can You Solve This Good Problem From Narayana Hyderabad Test
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Sir one more method using parametric coordinates...
Assume a point P(ct, ct, root(2)/ct ).
Use distance formula to find distance as a function of t and differentiate it
You'll get t= +-1/c
Put that in P, you'll get P(1,1, root(2))
Therefore minimum distance = 2 😊
ANOTHER GOOD METHOD 🎉
Very nice, but how did you think of taking this as the parametric point? Because its assuming x=y
@@_ehhwe can assume anything as Long as it satisfies the equation. Assuming x equal to y is not required but in this case it's quite intuitive to do so.
@@Radi-ux4st that is true, but what if there was a closer point where x≠y? Then wouldn't your method have failed to find the minima?
@@_ehh Ur right, but in this curve u can say it's symmetric abt y equals x. If u plot the graph u can see it.
Who all came after seeing NARAYANA in the thumbnail 😅
Keep uploading these type of video sir we love your channel ❤
Using am gm inequality (x²+y²+z²/2+z²/2)/4 greater than or equal to (x²y²z⁴/4)¼. We get directly without taking parametric form
You are a real inspiration for us
Awesome, lovely. Sir you are great
Excellent approach Sir
consider parameter (a,b,root(2/ab)) and then apply rms >= gm.
To min x,y,z possible value of x,yand z are 1,1and 2^1/2 and solve and we get answer 2
Sir Maine aisa hi socha ta lekin mene rms >am Kiya x,y,z aur phas gaya jabki Mujhe aap jaisa karnataka chalice tha
yes sir i wrote d square as x sq +y sq +2/xy and then applied am gm for x aND y ,got correct answer
Multivariate calculus (Maximum/minimum for 2 variable se vi solved kiya ja sakta he)
I did it in a way smarter and shorter way sir ... Actually put z²=2/xy and then form sqrt (x-y)² + 2/xy + 2xy ) x-y)² min value is zero and 2xy +2/xy will be greater equal to to which brings minimum value to √2×2
You need am-gm at the end anyways. Using am-gm directly is way shorter than what you did, sir elaborated every step otherwise it's a one-liner.
Solved this question in 2 min in mind. Took x=(root2)/t, y=(root2)/t , z= t paramatric points, direct substituting in distance formula and using AM GM condition.
Note: why i took x =y in paramatric is that if you get perfection with subject you will definitely find it's justfying. Visualize 3d, you will find only this possiblity as nearest to origin.
Very nice question sir & superb solution ❤🔥
Sir what a deep thinking
This q was first asked in FIITJEE CHD. JEE MAIN TEST SERIES
Sir after giving first look to this Question, One thing that came into my mind is to take values of x y and z as 1,1 and root2 and got 2 , although we were having a devil option[D] but can surely think like this to Eliminate Options
Same
It wrong approach only for this question (otherwise this work greatly)as we have to find minimum distance
Same😂😂
Thank you so much sir ..
because of you my math solving approach and ability has been increased so much, I am follwing you since a long time and It has helped me alot.
Anuj Mishra[JEE2025]
Love from Varanasi❤...
This video is very helpful for me
Max Min problems in geometry is very interesting. Solving without calculus, by using inequalities makes it even more interesting. You develop an intuition that's priceless. None can teach you that, none can buy you that. You develop it by solving on your own, thinking about a problem, trying variations of same problem. Thanks for posting Sir .
I also tried using inequality
We can use parametric form substitute x= t √2 = y and z=1/t then distance from (0,0,0) then use minima using differentiation we get point(1,1,√2)
Sir guess kiya tha AM GM se krna hai and got answer equal to 2. Achcha q hai sir, but I didn't see this one in all of my Narayana test papers.
Love from Pakistan 🇵🇰
The effort you put to teach us is admirable.
Keep up the good work 👍
Sir can we do it through RMS >= GM ??
Sir aapne 0 ki power 0 vali video mai kaha ki ye define nahi hai but aap sir usko (x-x)^(y-y) loge to (x-x)^(y)/(x-x)^(y) =1 to sahi to hai 1 ans hi aana chahiye sir aapne x^0=1 vali video mai bhi bataya tha
sir sabse phele hit and trial kiya vaha se sidha dikh gaya tha ki z root 2 se aaram se aajayega minimum distance but vo surity nahi de raha tha thn mene AM GM se he kiya tha
Sir I was having a problem in th given question
[x+(20x+100)^1/2]^1/2 +[x-(20x+100)^1/2]^1/2
=ax+b(c)^1/2
Then find the vale of a+b+c
it could be done as x²+y²+z² needs to minimised(the distance from the (0,0,0) therefore apply a.m inequality in which (x²+y²+z²/2+z^2/2)/4>(x²y²z⁴/4)¼ theredore x²+y²+z²>4 and thus the minimum distace will be 2.
Exactly, AM-GM inequality came in my mind too
I also solved this way bro
I looked at cross sections by setting z as a constant and rect hyperbola aya in xy plane jiska closest point to origin is related to z and i formed distance formula and differentiated
Although this has an assumption that rect hyperbola ka closest point to origin will be the closest in 3d plane for some z
I did it in the same way but 1 thing I would like to correct is that it is not an assumption that the minimum distance will be corresponding to the minimum distance of hyperbola from origin because: if the closest point were to be something other than that, I can always find a distance shorter than that by correspondingly increasing or decreasing the slope until I reach the point along the common normal with (0,0,t) where z=t is the plane of hyperbola
Its real problem ur solution excellsent
Sir mujhme calibre to bohot tha but na family support tha aur na financial support 🙂
Sir what i did was i put am gm on x^2 y^2 and z^2
x^2+y^2+z^2≥3(xyz) ^2/3
This implies that minimum will be acheived when x=y=z
Now xyz^2=2
And x=y=z
x=2^(1/4)
x^2 +y^2+z^2=3√2
Sir where did i went wrong? Can you tell my mistake?
take x as 1 y as 1 and z as root 2 then the minimum distance will be 2
these type of questions can be solved by using trial and error method in less than 30 secs
for a symmetric function x,y= 1, z = sqrt(2),
2 answer
Symmetric function? Can you explain?
@@gauravsalunke6045taking x equals y makes it symmetric as you replace x and y u get the same thing. This is method is usually used in curves which has center as origin. Cannot be always used tho.
@@Radi-ux4st oh thanks
Let's take (1,1,√2) satisfying the curve and it's distance from origin is 2 hence it is the answer
mene bhi aise kiya
dear sir what i did is
z^2 = 2/xy so d = ( 2/xy + x^2+y^2)^1/2 then x^2+y^2 >= 2xy so d>= root( 2xy+2/xy) so d>= 2 .... usually minimum maximum cases symetric hote hai ,,,, my 1st thing i did was x=y=1 and z =rt jisse 2 aagya tha then i did this 2nd method then watcher urs ,,,,,,, jabhi maths mai kuch nhi hota tab AM GM hi hota hai xd
I'm from narayana Hyderabad 😂
Nenu kuda bro
Hyderabadi boy living in North fan of Aman sir❤✌️
i am from bengal i am also a fan of aman sir
@@kridhameera7548 bro people thought we Bengals are not a part of India😂
west bengal ki baat kar raha main@@Afrin2005
west bengal ke baare mai bhi yahisochte kya @@Afrin2005
@@kridhameera7548 hmm vai tai e lage
Sir simply agar Sirf ek hi condition given hai toh am greater equal to Gm kardo
This question is in Engineering 1st Sem like about finding it from maxima Minima Concept
Sir plz make a video on am-gm inequality general proof.
Sir my first thought was AM-GM but then I solved it by observation I thought of 2 values for (x,y,z) which were (1,1,root2) and (1,2,1) both of which lie on the 3-D curve. Clearly the first set of values will have minimum distance which will be 2 and since the lowest value in the options is A that is 2 which also happens to be our answer (although later I realised none of these was also there lol)
"chinese solution" for this question
Olympiad questions pa video banaya sir
Sir aapse request h ki jee advance keliye New series laye
Aap jaisa pdhate ho kahani aur scientist ke bare mein btake waise hi advance level ka pdhaiye aur sir
Hame us level ki thinking dijiye jaise aap sochte ho maths ke bare mein
Similar ques in narayana module
Done by same approach 😊
Sir I know it is not feasible way. But can we solve the ques by trigonometry, by assuming an angle gamma with z axis and taking components of the position vector of point 'P'. And getting value of x, y, z on term of angle gamma and alpha[the angle of '' d sin(gamma) '' vector with x axis.
x=d sin(gamma) cos(alpha)
y=d sin(gamma) sin(alpha)
z=d cos(gamma)
And the finally putting values in equation : xyz² = 2.
I got d = 2÷[sin( 2 alpha). sin²(2 gamma) ]^¼
easy problem I SOLVED IT BY HYPERBOLA xy=2/z^2
Minimum distance=2/modz
Then using pythogoras sqrt(4/z^2+z^2)
then AM GM as 4/z^2 and z^2 are positive SO modz^2=2
So min distance=sqrt(2+2) =2+ANS
It is very elegant
I feel good solving this
Please like this so that everyone can learn this method also
It requires some 3d visualisation
Sir pair od straigt lines phadaiye
Mja aa gya bilkul ❤
id just use constrained optimization this is too complicated for me😅
Kya sir, lagrange multiplier se kr lo, maine 3min me solve kr diya
Can also do it by consider the given equation an equipotential surface and by partial differentiating we get eqn of normal in form of electric field vector
Can you explain more????
Consider xyz²=2 as an equipotential surface
Partial differentiating wrt x y &z gives us electric field vector :
yz²i+xz²j+2xyk
It's just gives direction of normal vector from origin so least distance point will pass through this line (as its surface would be perpendicular to normal )
Now equate
x=kyz²
y=kxz²
z=k2xyz
Find x y z in terms of k and then put them in given equation in question (we took k because we knew only direction)
Sir can we do it by Root mean square
2 is the answer by am-gm inequlity
Sir if we use logic xyz^2 =2 then 2 no.s will be one or minus one. And one no. Will be 2. 2*1=2… therefore ans 2.. 😂
Done it in the same way😊
I also study in Narayana Mumbai studying JEE in 8th grade
same method me solve kiya tha 👍👍👍👍❤❤❤
❤❤❤
Sir apne MIT intrigation ka problem ka solution diya nahi 😢
Anything about jee 2025
Iam too from Hyderabad and also narayana sir they provide lots of questions like this pls do videos on them
HI BRO WHICH BRANCH
@@gameoftrading4051 naryana housing board
I did this question. I am from CO spark batch
Weighted AM GM
Easy peasy 😊
If sir was teaching chess instead of maths then basically he is saying ' ki beta stockfish toh soch leta hai toh tumko nahi soch rahe ho utna ye toh kitna common hai ' (in this particular video not always )😂😂
God tussi great ho awesome 👍👍 Jai hind sir Deepak Lucknow
Easy peasy....
I am from Narayana Hyderabad
Fiitjee GMP question
Sir why Z2 /2 and Z2/2
I am from Hitex division branch 🤓
Hitech city
Fiitjee gmp problem❤
Any one telugu here
Am ≥ GM se kardiya sir
I opened video .... Paused it....
Took 3 minutes....
Here is what I done....
Let (a,b,c) are the points that lie on curve nearest from origin.....
distance = (a²+b²+c²)½
Now using AM > = GM
a²+b²+c²/2+c²/2/4 >= (2²/2²)¼
a²+b²+c² >= 4
This min distance = 2
Let's see sir ki approach and correct answer
I thought kuch naya kiya hoga maine but sir ke jaisa hi hua same😭
Hello sir
2
A
Solved it by same method on first attempt
Have you solve it without help?
Quadratic mean >= gm
AM GM
Sir power ma 1/4 kaisa hua??
GM ka formula hoga wo
Narayana Bolthe
Bhannat
Another method... Since minimum distance should be taken in a path of a straight line
Three cases arise to consist low(1 as integer) magnitude integer maximum number of times
(1,1,√2) or (2,1,1) or (1,2,1)
Since it should be minimum
(1,1,√2) is taken as its distance from origin is 2....
Simple....
sir sabse acha hai ki x=1,y=1 aur z=root 2 put kardege. Answer aa jayega😃
sir can we do by parameters, (2t,t,1/t)???
No bro
Yes, I also did by assuming parameter t
Ans is coming 2
Yes it's possible
Telangana viewers like here ✅
Narayana k student presenti lagao 🖐
😙😙😙😙for any fix value of z there is rectangular hyperbola in x y plane ab jo rect. Hyperbola hai usko x=y straight line se cut krane pr jo point milenge wo toh pka origin ke paas honge now ab solve krne ke liye let z=p then rect. Hyperbola is xy=2/p^2 or x=y or hyperbola ko solve krne pr hme milega ga thenga😅 oh sorry hme milega y=√2/p =x .......😴😴 now we have only one variable that is p required thing is( x^2+ y^2 +z^2)^1/2 .... .,.,.,.,.,. ❤❤❤ now put x=y=√2/p and z= 2 as above mentioned then differentiate w.r.t p to get minima😊😊😊 question is dead🎉🎉🎉🎉🎉🎉😮😮😮😮❤❤❤❤
Itna asan qs ko itna bada chade ke video bana band karo yar
Then there is me who got the AM GM correctly but forgot to take the root